Rendezvous problem for chains of kinematic points

Abstract

AbstractThis paper studies the dynamic of a chain of infinitely many kinematic points guaranteeing the uniform convergence in the sense. A sufficient condition and some necessary conditions for infinite many kinematic points rendezvousing are given in terms of the spectrum and the invariant subspaces of the dynamic operator. The necessary and sufficient condition for finitely many kinematic points rendezvousing is characterized by the eigenvalues and the invariant subspaces of the dynamic operator. The estimate on the rate of the rendezvous is derived based on the spectrum of the dynamic operator.